How do dentists decide when to do an implant?

Careful planning! Implants in dentistry are anchors that are made of titanium and fuse to the jaw bone after being placed. A dentist needs to carefully evaluate your unique situation ( missing 1 tooth, several or all) and discuss with the benefits of using implants in your unique situation. Than other option might be discussed, but hopefully you can both come to the best solution for your needs.
A number of factors. We look at is if there is adequate bone to support an implant, as well as enough space. We also look at your risk factors such a smoking and diabetes. We also need to take into account, how you bite, what would be opposing the implant, and aesthetic concerns. We also need to rule out other treatments and condition of surrounding teeth in which some cases it may be better to do a bridge.
Patients decision. It is our job (dentist) to educate and present options. Any time a tooth is missing (not wisdom teeth), there is enough bone, or the potential for grafting enough bone and there is no health concerns, an implant is likely an option. It needs to improve function or esthetics in order for it to be a recomendation in our office. We give options for our patients to make the final decision from.
Different factors. Implants replace missing teeth, so any time there is a tooth to be extracted or already missing, is a time to consider implant. Sometimes, implants are considered as an alternative to root canal and crown procedure. There are many factors in addition, such as contraindications to patient having an implant (systemic health issues), bite considerations, patient maintenance. Discuss with your doc.